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Class 10MathematicsReal NumbersDecimal expansion of rational numbersExpertLevel 20
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If (n) is the smallest positive integer for which (\frac{n}{2^5\cdot 3^2\cdot 5^3\cdot 7^2}) has a terminating decimal, what is (n)?

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Answer and explanation

Correct answer: (441)

For termination, (3^2) and (7^2) must cancel completely, so (n=441). For the least value, cancel only the factors other than (2) and (5).

Related tags

Minimum-FactorTerminating-ConditionPrime-FactorisationReal-Numbers

Frequently asked questions

What is the correct answer to this question?

(441)

Why is this the correct answer?

For termination, (3^2) and (7^2) must cancel completely, so (n=441). For the least value, cancel only the factors other than (2) and (5).

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Decimal expansion of rational numbers.

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  1. 1What type of decimal expansion will the rational number (\frac{3}{8}) have?
  2. 2What type of decimal expansion does (\frac{5}{6}) have?
  3. 3Under what condition does (\frac{p}{q}) have a terminating decimal expansion when the fraction is in lowest form?
  4. 4After reducing (\frac{15}{40}), what type of decimal expansion will it have?
  5. 5After at most how many decimal places will the decimal expansion of (\frac{7}{16}) terminate?
  6. 6Choose the correct statement about the decimal expansion of (\frac{11}{45}).
  7. 7Which of the following fractions will give a terminating decimal?
  8. 8Which of the following fractions will give a non-terminating recurring decimal?
  9. 9When (0.75) is written as a rational number, which form is obtained?
  10. 10If the denominator of a fraction in lowest form is (2^3\times5^2), after at most how many decimal places will its decimal expansion terminate?
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